{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE StrictData #-}
{-# LANGUAGE TypeFamilies #-}
{-# OPTIONS_GHC -Wall #-}
{-# OPTIONS_GHC -fno-warn-type-defaults #-}
module Box.Box
( Box (..),
CoBox,
CoBoxM (..),
bmap,
foistb,
glue,
glueN,
fuse,
Divap (..),
DecAlt (..),
cobox,
seqBox,
)
where
import Box.Committer
import Box.Emitter
import Control.Applicative
( Alternative (empty, (<|>)),
Applicative (liftA2),
)
import Data.Functor.Contravariant (Contravariant (contramap))
import Data.Functor.Contravariant.Divisible
( Decidable (choose, lose),
Divisible (conquer, divide),
)
import Data.Profunctor (Profunctor (dimap))
import Data.Void (Void, absurd)
import Prelude hiding ((.), id)
import Box.Codensity
import Control.Monad.State.Lazy
import qualified Data.Sequence as Seq
import Data.Bool
import Data.Semigroupoid
import Box.Functor
data Box m c e = Box
{ Box m c e -> Committer m c
committer :: Committer m c,
Box m c e -> Emitter m e
emitter :: Emitter m e
}
foistb :: (forall a. m a -> n a) -> Box m c e -> Box n c e
foistb :: (forall a. m a -> n a) -> Box m c e -> Box n c e
foistb forall a. m a -> n a
nat (Box Committer m c
c Emitter m e
e) = Committer n c -> Emitter n e -> Box n c e
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box ((forall a. m a -> n a) -> Committer m c -> Committer n c
forall (h :: (* -> *) -> * -> *) (f :: * -> *) (g :: * -> *) a.
FFunctor h =>
(forall x. f x -> g x) -> h f a -> h g a
foist forall a. m a -> n a
nat Committer m c
c) ((forall a. m a -> n a) -> Emitter m e -> Emitter n e
forall (h :: (* -> *) -> * -> *) (f :: * -> *) (g :: * -> *) a.
FFunctor h =>
(forall x. f x -> g x) -> h f a -> h g a
foist forall a. m a -> n a
nat Emitter m e
e)
instance (Functor m) => Profunctor (Box m) where
dimap :: (a -> b) -> (c -> d) -> Box m b c -> Box m a d
dimap a -> b
f c -> d
g (Box Committer m b
c Emitter m c
e) = Committer m a -> Emitter m d -> Box m a d
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box ((a -> b) -> Committer m b -> Committer m a
forall (f :: * -> *) a b. Contravariant f => (a -> b) -> f b -> f a
contramap a -> b
f Committer m b
c) ((c -> d) -> Emitter m c -> Emitter m d
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap c -> d
g Emitter m c
e)
instance (Alternative m, Monad m) => Semigroup (Box m c e) where
<> :: Box m c e -> Box m c e -> Box m c e
(<>) (Box Committer m c
c Emitter m e
e) (Box Committer m c
c' Emitter m e
e') = Committer m c -> Emitter m e -> Box m c e
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box (Committer m c
c Committer m c -> Committer m c -> Committer m c
forall a. Semigroup a => a -> a -> a
<> Committer m c
c') (Emitter m e
e Emitter m e -> Emitter m e -> Emitter m e
forall a. Semigroup a => a -> a -> a
<> Emitter m e
e')
instance (Alternative m, Monad m) => Monoid (Box m c e) where
mempty :: Box m c e
mempty = Committer m c -> Emitter m e -> Box m c e
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box Committer m c
forall a. Monoid a => a
mempty Emitter m e
forall a. Monoid a => a
mempty
mappend :: Box m c e -> Box m c e -> Box m c e
mappend = Box m c e -> Box m c e -> Box m c e
forall a. Semigroup a => a -> a -> a
(<>)
bmap :: (Monad m) => (a' -> m (Maybe a)) -> (b -> m (Maybe b')) -> Box m a b -> Box m a' b'
bmap :: (a' -> m (Maybe a))
-> (b -> m (Maybe b')) -> Box m a b -> Box m a' b'
bmap a' -> m (Maybe a)
fc b -> m (Maybe b')
fe (Box Committer m a
c Emitter m b
e) = Committer m a' -> Emitter m b' -> Box m a' b'
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box ((a' -> m (Maybe a)) -> Committer m a -> Committer m a'
forall (m :: * -> *) b a.
Monad m =>
(b -> m (Maybe a)) -> Committer m a -> Committer m b
witherC a' -> m (Maybe a)
fc Committer m a
c) ((b -> m (Maybe b')) -> Emitter m b -> Emitter m b'
forall (m :: * -> *) a b.
Monad m =>
(a -> m (Maybe b)) -> Emitter m a -> Emitter m b
witherE b -> m (Maybe b')
fe Emitter m b
e)
glue :: (Monad m) => Committer m a -> Emitter m a -> m ()
glue :: Committer m a -> Emitter m a -> m ()
glue Committer m a
c Emitter m a
e = (m () -> m ()) -> m ()
forall a. (a -> a) -> a
fix ((m () -> m ()) -> m ()) -> (m () -> m ()) -> m ()
forall a b. (a -> b) -> a -> b
$ \m ()
rec -> Emitter m a -> m (Maybe a)
forall (m :: * -> *) a. Emitter m a -> m (Maybe a)
emit Emitter m a
e m (Maybe a) -> (Maybe a -> m Bool) -> m Bool
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= m Bool -> (a -> m Bool) -> Maybe a -> m Bool
forall b a. b -> (a -> b) -> Maybe a -> b
maybe (Bool -> m Bool
forall (f :: * -> *) a. Applicative f => a -> f a
pure Bool
False) (Committer m a -> a -> m Bool
forall (m :: * -> *) a. Committer m a -> a -> m Bool
commit Committer m a
c) m Bool -> (Bool -> m ()) -> m ()
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= m () -> m () -> Bool -> m ()
forall a. a -> a -> Bool -> a
bool (() -> m ()
forall (f :: * -> *) a. Applicative f => a -> f a
pure ()) m ()
rec
glueN :: Monad m => Int -> Committer m a -> Emitter m a -> m ()
glueN :: Int -> Committer m a -> Emitter m a -> m ()
glueN Int
n Committer m a
c Emitter m a
e = (StateT Int m () -> Int -> m ()) -> Int -> StateT Int m () -> m ()
forall a b c. (a -> b -> c) -> b -> a -> c
flip StateT Int m () -> Int -> m ()
forall (m :: * -> *) s a. Monad m => StateT s m a -> s -> m a
evalStateT Int
0 (StateT Int m () -> m ()) -> StateT Int m () -> m ()
forall a b. (a -> b) -> a -> b
$ Committer (StateT Int m) a
-> Emitter (StateT Int m) a -> StateT Int m ()
forall (m :: * -> *) a.
Monad m =>
Committer m a -> Emitter m a -> m ()
glue ((forall x. m x -> StateT Int m x)
-> Committer m a -> Committer (StateT Int m) a
forall (h :: (* -> *) -> * -> *) (f :: * -> *) (g :: * -> *) a.
FFunctor h =>
(forall x. f x -> g x) -> h f a -> h g a
foist forall x. m x -> StateT Int m x
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift Committer m a
c) (Int -> Emitter m a -> Emitter (StateT Int m) a
forall (m :: * -> *) a.
Monad m =>
Int -> Emitter m a -> Emitter (StateT Int m) a
takeE Int
n Emitter m a
e)
fuse :: (Monad m) => (a -> m (Maybe b)) -> Box m b a -> m ()
fuse :: (a -> m (Maybe b)) -> Box m b a -> m ()
fuse a -> m (Maybe b)
f (Box Committer m b
c Emitter m a
e) = Committer m b -> Emitter m b -> m ()
forall (m :: * -> *) a.
Monad m =>
Committer m a -> Emitter m a -> m ()
glue Committer m b
c ((a -> m (Maybe b)) -> Emitter m a -> Emitter m b
forall (m :: * -> *) a b.
Monad m =>
(a -> m (Maybe b)) -> Emitter m a -> Emitter m b
witherE a -> m (Maybe b)
f Emitter m a
e)
class Divap p where
divap :: (a -> (b, c)) -> ((d, e) -> f) -> p b d -> p c e -> p a f
conpur :: a -> p b a
instance (Applicative m) => Divap (Box m) where
divap :: (a -> (b, c))
-> ((d, e) -> f) -> Box m b d -> Box m c e -> Box m a f
divap a -> (b, c)
split' (d, e) -> f
merge (Box Committer m b
lc Emitter m d
le) (Box Committer m c
rc Emitter m e
re) =
Committer m a -> Emitter m f -> Box m a f
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box ((a -> (b, c)) -> Committer m b -> Committer m c -> Committer m a
forall (f :: * -> *) a b c.
Divisible f =>
(a -> (b, c)) -> f b -> f c -> f a
divide a -> (b, c)
split' Committer m b
lc Committer m c
rc) ((d -> e -> f) -> Emitter m d -> Emitter m e -> Emitter m f
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (((d, e) -> f) -> d -> e -> f
forall a b c. ((a, b) -> c) -> a -> b -> c
curry (d, e) -> f
merge) Emitter m d
le Emitter m e
re)
conpur :: a -> Box m b a
conpur a
a = Committer m b -> Emitter m a -> Box m b a
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box Committer m b
forall (f :: * -> *) a. Divisible f => f a
conquer (a -> Emitter m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
a)
class Profunctor p => DecAlt p where
choice :: (a -> Either b c) -> (Either d e -> f) -> p b d -> p c e -> p a f
loss :: p Void b
instance (Monad m, Alternative m) => DecAlt (Box m) where
choice :: (a -> Either b c)
-> (Either d e -> f) -> Box m b d -> Box m c e -> Box m a f
choice a -> Either b c
split' Either d e -> f
merge (Box Committer m b
lc Emitter m d
le) (Box Committer m c
rc Emitter m e
re) =
Committer m a -> Emitter m f -> Box m a f
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box ((a -> Either b c)
-> Committer m b -> Committer m c -> Committer m a
forall (f :: * -> *) a b c.
Decidable f =>
(a -> Either b c) -> f b -> f c -> f a
choose a -> Either b c
split' Committer m b
lc Committer m c
rc) ((Either d e -> f) -> Emitter m (Either d e) -> Emitter m f
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Either d e -> f
merge (Emitter m (Either d e) -> Emitter m f)
-> Emitter m (Either d e) -> Emitter m f
forall a b. (a -> b) -> a -> b
$ (d -> Either d e) -> Emitter m d -> Emitter m (Either d e)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap d -> Either d e
forall a b. a -> Either a b
Left Emitter m d
le Emitter m (Either d e)
-> Emitter m (Either d e) -> Emitter m (Either d e)
forall (f :: * -> *) a. Alternative f => f a -> f a -> f a
<|> (e -> Either d e) -> Emitter m e -> Emitter m (Either d e)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap e -> Either d e
forall a b. b -> Either a b
Right Emitter m e
re)
loss :: Box m Void b
loss = Committer m Void -> Emitter m b -> Box m Void b
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box ((Void -> Void) -> Committer m Void
forall (f :: * -> *) a. Decidable f => (a -> Void) -> f a
lose Void -> Void
forall a. Void -> a
absurd) Emitter m b
forall (f :: * -> *) a. Alternative f => f a
empty
type CoBox m a b = Codensity m (Box m a b)
cobox :: CoCommitter m a -> CoEmitter m b -> CoBox m a b
cobox :: CoCommitter m a -> CoEmitter m b -> CoBox m a b
cobox CoCommitter m a
c CoEmitter m b
e = Committer m a -> Emitter m b -> Box m a b
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box (Committer m a -> Emitter m b -> Box m a b)
-> CoCommitter m a -> Codensity m (Emitter m b -> Box m a b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> CoCommitter m a
c Codensity m (Emitter m b -> Box m a b)
-> CoEmitter m b -> CoBox m a b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> CoEmitter m b
e
seqBox :: (Monad m) => Box (StateT (Seq.Seq a) m) a a
seqBox :: Box (StateT (Seq a) m) a a
seqBox = Committer (StateT (Seq a) m) a
-> Emitter (StateT (Seq a) m) a -> Box (StateT (Seq a) m) a a
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box Committer (StateT (Seq a) m) a
forall (m :: * -> *) a. Monad m => Committer (StateT (Seq a) m) a
push Emitter (StateT (Seq a) m) a
forall (m :: * -> *) a. Monad m => Emitter (StateT (Seq a) m) a
pop
dotco :: Monad m => Codensity m (Box m a b) -> Codensity m (Box m b c) -> Codensity m (Box m a c)
dotco :: Codensity m (Box m a b)
-> Codensity m (Box m b c) -> Codensity m (Box m a c)
dotco Codensity m (Box m a b)
b Codensity m (Box m b c)
b' = m (Box m a c) -> Codensity m (Box m a c)
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (m (Box m a c) -> Codensity m (Box m a c))
-> m (Box m a c) -> Codensity m (Box m a c)
forall a b. (a -> b) -> a -> b
$ do
(Box Committer m a
c Emitter m b
e) <- Codensity m (Box m a b) -> m (Box m a b)
forall (f :: * -> *) a. Applicative f => Codensity f a -> f a
lowerCodensity Codensity m (Box m a b)
b
(Box Committer m b
c' Emitter m c
e') <- Codensity m (Box m b c) -> m (Box m b c)
forall (f :: * -> *) a. Applicative f => Codensity f a -> f a
lowerCodensity Codensity m (Box m b c)
b'
Committer m b -> Emitter m b -> m ()
forall (m :: * -> *) a.
Monad m =>
Committer m a -> Emitter m a -> m ()
glue Committer m b
c' Emitter m b
e
Box m a c -> m (Box m a c)
forall (f :: * -> *) a. Applicative f => a -> f a
pure (Committer m a -> Emitter m c -> Box m a c
forall (m :: * -> *) c e. Committer m c -> Emitter m e -> Box m c e
Box Committer m a
c Emitter m c
e')
newtype CoBoxM m a b = CoBoxM { CoBoxM m a b -> Codensity m (Box m a b)
uncobox :: Codensity m (Box m a b) }
instance (Monad m) => Semigroupoid (CoBoxM m) where
o :: CoBoxM m j k1 -> CoBoxM m i j -> CoBoxM m i k1
o (CoBoxM Codensity m (Box m j k1)
b) (CoBoxM Codensity m (Box m i j)
b')= Codensity m (Box m i k1) -> CoBoxM m i k1
forall (m :: * -> *) a b. Codensity m (Box m a b) -> CoBoxM m a b
CoBoxM (Codensity m (Box m i j)
-> Codensity m (Box m j k1) -> Codensity m (Box m i k1)
forall (m :: * -> *) a b c.
Monad m =>
Codensity m (Box m a b)
-> Codensity m (Box m b c) -> Codensity m (Box m a c)
dotco Codensity m (Box m i j)
b' Codensity m (Box m j k1)
b)